Finite Precision Number Systems and Arithmetic

This comprehensive reference volume, suitable for graduate teaching, includes problems, exercises, solutions and an extensive bibliography.

Peter Kornerup (Author), David W. Matula (Author)

9780521761352, Cambridge University Press

Hardback, published 30 September 2010

716 pages, 155 b/w illus. 70 tables 240 exercises
24.1 x 16.3 x 4.1 cm, 1.21 kg

'For researchers and more mathematically oriented readers, this book is a treasure trove of algorithms difficult or impossible to find elsewhere.' Mathematical Reviews

Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for graduate teaching: problems and exercises are scattered throughout the text and a solutions manual is available for instructors.

Preface
1. Radix polynomial representations
2. Base and digit set conversion
3. Addition
4. Multiplication
5. Division
6. Square root
7. Floating point number systems
8. Modular arithmetic and residue number systems
9. Rational arithmetic
Author index
Index.

Subject Areas: Maths for scientists [PDE], Numerical analysis [PBKS]